A robust optimization design method for asymmetric rail profile on railway small radius curves

Abstract

The present invention provides a robust optimization design method for asymmetric rail profiles on railway small radius curves, which relates to the technical field of rail profile optimization, including obtaining multiple groups of random samples; constructing a coupled dynamics simulation model of a vehicle-track system according to the random samples to output key indicators, the key indicators including wheel-rail force, derailment coefficient, wheel weight reduction rate and rail wear; calculating the rail cumulative wear depth data under different random variable combinations according to the key indicators and a preset wear model; constructing a dynamic response prediction model according to the random samples, the key indicators and the rail cumulative wear depth data; using the random samples as the input values ​​of the dynamic response prediction model to obtain probability density distribution results, and performing sensitivity analysis to obtain sensitive variables; generating a Pareto front solution according to the sensitive variables and the preset design variables, and fitting to obtain a rail profile optimization design scheme. The present invention realizes that the rail profile optimization solution adapts to a complex and random operating environment.

Description

Technical Field

[0001] The invention relates to the technical field of rail profile optimization, and in particular to a robust optimization design method for an asymmetric rail profile on a railway small-radius curve. Background Art

[0002] Most rail transit lines are built in medium and large cities with limited land resources. These subway lines often have many small-radius curves. The rapid development of small-radius curve rail side wear will directly reduce the curve passing performance of trains and shorten the service life of rails.

[0003] Small radius curves increase the possibility of wheel-rail lateral forces and wheel-rail interactions. These forces will accelerate rail wear and reduce the running quality of the train, leading to a series of problems that will undermine the integrity and safety of railway operations. Personnel in related technical fields have carried out profile optimization design of rails and wheels, which has played a certain role in improving vehicle performance and wheel-rail service life. However, with the long-term operation of vehicles and track structures, vehicle and track parameters have strong uncertainty. The obtained rail profile optimization solution is difficult to adapt to the complex and random operating environment, and the guiding rail grinding effect is unsatisfactory.

[0004] Therefore, how to achieve rail profile optimization to adapt to the complex and random operating environment is an urgent problem to be solved in this technical field. Summary of the invention

[0005] The purpose of the present invention is to provide a method for optimizing the robustness of asymmetric rail profiles on small-radius railway curves to improve the above-mentioned problems. In order to achieve the above-mentioned purpose, the technical solutions adopted by the present invention are as follows:

[0006] The present application provides a method for optimizing the robustness of an asymmetric rail profile for a railway small radius curve, comprising:

[0007] Obtaining a wear variable range of rail profile geometry, a vehicle parameter variable range, and a track parameter variable range, and generating multiple groups of random samples through Latin hypercube according to the wear variable range, the vehicle parameter variable range, and the track parameter variable range;

[0008] Constructing a coupled dynamics simulation model of a vehicle-track system according to the random samples, and outputting key indicators by simulating the dynamic response of the vehicle-track system, wherein the key indicators include the wheel-rail force, derailment coefficient, wheel load reduction rate and rail wear of each of the random samples;

[0009] Calculating the rail cumulative wear depth data under different random variable combinations according to the key indicators and the preset wear model;

[0010] A proxy model is constructed according to the random sample, the key index and the rail cumulative wear depth data, and the proxy model is optimized, and the coupled dynamics simulation model is substituted by the optimized proxy model to obtain a dynamic response prediction model;

[0011] The random samples are used as input values ​​of the dynamic response prediction model, and the probability density distribution results of the rail wear performance and the wheel-rail dynamic response are obtained by predicting the dynamic response and wear depth under random working conditions, and a sensitivity analysis is performed on the probability density distribution results to obtain sensitive variables that affect the optimization target;

[0012] A multi-objective function is constructed according to the sensitive variables and the preset design variables to generate a Pareto front solution, and a rail profile optimization design scheme is obtained based on the Pareto front solution fitting.

[0013] The beneficial effects of the present invention are:

[0014] The present invention predicts the geometric profile of the rail under complex and random operating conditions through a wear prediction algorithm. According to the predicted profile and its corresponding dynamic performance, a reasonable rail grinding strategy can be formulated, which is conducive to reasonably guiding the grinding of the rail profile, improving the service life of the rail, and realizing the optimization solution of the rail profile to adapt to the complex and random operating environment.

[0015] Other features and advantages of the present invention will be described in the following description, and partly become apparent from the description, or be understood by implementing the embodiments of the present invention. The purpose and other advantages of the present invention can be realized and obtained by the structures particularly pointed out in the written description, claims, and drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without creative work.

[0017] Figure 1 This is a flow chart of the robustness optimization design method for asymmetric rail profile on a railway small radius curve described in this application;

[0018] Figure 2 It is a discrete schematic diagram of the rail profile on the high rail side;

[0019] Figure 3 It is a discrete schematic diagram of the rail profile on the low rail side;

[0020] Figure 4This is the optimization flow chart of the hunter-prey intelligent optimization algorithm of this application;

[0021] Figure 5 This is the optimization flow chart of the particle swarm intelligent optimization algorithm of this application;

[0022] Figure 6 This is a schematic diagram of the prediction accuracy of the high rail side;

[0023] Figure 7 This is a schematic diagram of the prediction accuracy of the low-orbit side;

[0024] Figure 8 This is a schematic diagram of the comparison of proxy models in the test set;

[0025] Fig. 9 A schematic diagram showing the comparison of proxy models in the training set;

[0026] Fig.10 A schematic diagram of the slope relationship of data points on the rail profile of this application;

[0027] Fig.11 A schematic diagram of the Pareto front for this application;

[0028] Fig.12 Schematic diagram of marginal probability density function distribution of lateral wheel-rail force under random operating conditions of this application;

[0029] Fig.13 Schematic diagram of marginal probability density function distribution of cumulative wear depth of rail under random operating conditions of this application;

[0030] Fig.14 This is a schematic diagram comparing the rail wear depth before and after optimization;

[0031] Fig.15 Schematic diagram of the comparison of lateral wheel-rail forces before and after optimization;

[0032] Fig.16 A schematic diagram showing the comparison of the derailment coefficients on the high rail side before and after optimization;

[0033] Fig.17 This is a schematic diagram comparing the wear work on the high rail side before and after optimization;

[0034] Fig.18 This is a schematic diagram showing the comparison of the wear of the high rail side rail profile before and after optimization after the vehicle passes 100,000 times;

[0035] Fig.19 Schematic diagram showing the comparison of the wear of the low-rail side rail profile before and after optimization after the vehicle passes 100,000 times. DETAILED DESCRIPTION

[0036] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. The components of the embodiments of the present invention generally described and shown in the drawings here can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0037] It should be noted that similar reference numerals and letters represent similar items in the following drawings, so once an item is defined in one drawing, it does not need to be further defined and explained in the subsequent drawings. At the same time, in the description of the present invention, the terms "first", "second", etc. are only used to distinguish the description and cannot be understood as indicating or implying relative importance.

[0038] like Figure 1 As shown, this embodiment provides a method for optimizing the robustness of an asymmetric rail profile for a railway small radius curve, including:

[0039] Step S100, obtaining a wear variable range of rail profile geometry, a vehicle parameter variable range, and a track parameter variable range, and generating multiple groups of random samples through Latin hypercube according to the wear variable range, the vehicle parameter variable range, and the track parameter variable range;

[0040] Step S200, constructing a coupled dynamics simulation model of a vehicle-track system according to the random samples, and outputting key indicators by simulating the dynamic response of the vehicle-track system, wherein the key indicators include the wheel-rail force, derailment coefficient, wheel load reduction rate and rail wear of each of the random samples;

[0041] Step S300, calculating the rail cumulative wear depth data under different random variable combinations according to the key indicators and the preset wear model;

[0042] Step S400, constructing a proxy model according to the random sample, the key index and the rail cumulative wear depth data, optimizing the proxy model, and using the optimized proxy model to proxy the coupled dynamics simulation model to obtain a dynamic response prediction model;

[0043] Step S500: using the random sample as the input value of the dynamic response prediction model, obtaining the probability density distribution results of the rail wear performance and the wheel-rail dynamic response by predicting the dynamic response and wear depth under random working conditions, and performing sensitivity analysis on the probability density distribution results to obtain sensitive variables that affect the optimization target;

[0044] Step S600: construct a multi-objective function according to the sensitive variables and the preset design variables to generate a Pareto front solution, and obtain a rail profile optimization design solution based on the Pareto front solution fitting.

[0045] It should be noted that the vehicle-track system has random operating conditions:

[0046] Consider random variables such as vehicle suspension parameters (primary stiffness / damping, secondary stiffness / damping), axle weight, running speed, wheel geometry, etc.; consider random variables such as wheel-rail friction coefficient, rail bottom slope, track gauge, fastener stiffness, and comprehensively consider the impact of these uncertain parameters on the optimization results.

[0047] Furthermore, the wear variables for determining the rail profile geometry in step S100 include:

[0048] Step S110, obtaining the optimized area parameters of the rail profile by analyzing the contact geometry between the rail profile and the wheelset;

[0049] Step S120, establishing a rail profile discrete coordinate system based on the optimization area parameters;

[0050] Step S130, discretely setting the optimization area parameters to a plurality of movable points in the rail profile discrete coordinate system, wherein the lateral coordinates of the movable points are fixed and the vertical coordinates of the movable points are variable;

[0051] Step S140, presetting a variable range of the vertical coordinates of the movable point, and using the variable range of the vertical coordinates of the movable point as a wear variable of the rail profile geometry.

[0052] It is understandable that when a vehicle passes over a curved rail, it is affected by the centrifugal force, and the wheel-rail contact geometry and mechanics of the left and right rails of the rail present strong asymmetry. Therefore, due to the asymmetric rolling contact, the rail profiles of the left and right rails also present obvious asymmetry. Before performing asymmetric robustness optimization on the rail profile of the curved section, the optimized areas of the left and right rails are first determined by analyzing the wheel-rail contact geometry. The optimized area is the area where the rails are polished. In the discrete coordinate system of the rail profile, the rail profile is divided into a non-optimized area and an optimized area. Several discrete points with fixed horizontal coordinates but variable vertical coordinates are selected as movable points, and the vertical coordinates of the movable points are used as design variables. ,like Figure 2-Figure 3 As shown in the figure, A and B are fixed points on the boundary of the optimization area. The area between A and B is the optimization area, and the area outside A and B is the non-optimization area. The optimization area of ​​the left rail and the right rail is discretized into 10 movable points respectively. The movable points on the high rail side are Indicates that the movable point on the low rail side is Indicates that To optimize the number of movable points in the area. According to the requirements of the on-site grinding operation, the amount of rail grinding It should be less than 1.0 mm, so the rail grinding variable value range is as follows:

[0053] ;

[0054] Based on the value range of the rail grinding variable, the variable range of the vertical coordinates of the movable point is preset to obtain the wear variable of the rail profile geometry. The wear variable of the high rail side is expressed as , the wear variable on the low rail side is expressed as .

[0055] Further, step S200 includes steps S210 to S230:

[0056] Step S210: acquiring vehicle parameters and track design parameters, and constructing a vehicle model based on the vehicle parameters, and constructing a track model based on the track design parameters;

[0057] Step S220, setting the body, frame and wheelset of the vehicle model to be steel bodies, and simulating the primary suspension and secondary suspension of the vehicle model according to the spring damping unit in the multi-body dynamics analysis software package;

[0058] Step S230: coupling the vehicle model and the track model to obtain the coupled dynamics simulation model, wherein the coupled dynamics simulation model uses the Hertz nonlinear contact algorithm for dynamics simulation, and the wheel-rail tangential contact of the coupled dynamics simulation model is solved by the Fastsim fast simulation algorithm.

[0059] It can be understood that the vehicle model consists of a vehicle body, a frame, a wheelset, and a primary suspension and a secondary suspension. The vehicle frame structure is basically the same, the primary suspension is a laminated rubber spring, and the secondary suspension includes two large damping air springs, a unilateral lateral shock absorber, two centrally symmetrical traction rods, and a lateral stopper. The nonlinear characteristics of the lateral stopper and the lateral shock absorber are considered.

[0060] In order to make the vehicle model as realistic as possible, highlight the key points and facilitate calculation and analysis, the vehicle-track modeling mainly considers: the car body, frame, and wheelset are all regarded as rigid bodies. The spring damping unit in the multi-body dynamics analysis software package is used to simulate the primary and secondary suspension systems; the wheel tread adopts the LM profile. The rail is the Chinese 60 kg / m profile. The vehicle consists of 15 rigid bodies, including 1 car body, 2 frames, 4 wheelsets, and 8 axle boxes. Among them, the car body, frame, and wheelset have 6 degrees of freedom, namely lateral, longitudinal, vertical, roll, nod, and shake. The axle box only has the nod degree of freedom. The entire vehicle model includes 50 degrees of freedom. The vertical motion and roll motion of the wheelset are non-independent motions, and the other motions are independent of each other.

[0061] The wheel-rail contact model is an important link for coupling the vehicle model and the track model. When simulating the dynamics of the vehicle passing through a curve, the Hertz nonlinear contact algorithm with higher computational efficiency is used, among which the wheel-rail tangential contact is solved by a fast simulation algorithm.

[0062] Further, step S300 includes step S310 to step S340;

[0063] Step S310, constructing an Archad wear model based on the key indicators;

[0064] Step S320: The Archad wear model assumes that the material wear behavior only occurs in the sliding area of ​​the contact patch, and no wear occurs in the adhesion area. The wheel-rail wear volume on the contact patch is calculated by the following formula:

[0065] ;

[0066] In the formula, is the wheel-rail wear volume on the contact patch, is the Archard wear coefficient, which is calculated from the contact stress and relative sliding velocity. is the normal contact stress, is the relative sliding distance, is the hardness of the wheel and rail material;

[0067] Step S330, dividing the contact spot into N grids, and using the following formula to solve the wear amount in each grid respectively;

[0068] Step S340: Based on the accumulated wear amounts in the N grids, the accumulated rail wear depth data of the rail profile under random operating conditions is obtained.

[0069] ;

[0070] In the formula, is the wear depth at the corresponding position of the contact spot; is the wear area; is the normal contact stress at the point; is the relative slip between wheel and rail.

[0071] The wear depth of rail profile under random operating conditions is predicted, and finally the mean and variance of rail wear parameters after the vehicle passes a certain curve 100,000 times are taken as optimization targets.

[0072] Further, step S400 includes step S410 to step S440;

[0073] Step S410: constructing a neural network proxy model based on the random sample, the key indicators and the rail cumulative wear depth data, wherein the neural network proxy model consists of an input layer, two hidden layers and an output layer, and the neural network proxy model uses a maximum-minimum normalization method to preprocess the sample data;

[0074] Step S420, 80% of the random samples of the key indicators are used to train the neural network proxy model as the objective function and constraint function;

[0075] Step S430: 20% of the random samples of the key indicators are used to test the neural network proxy model;

[0076] Step S440: The neural network proxy model uses a maximum-minimum normalization method to preprocess the sample data.

[0077] It is understandable that the existing technology only considers the geometric coordinates of the wheel-rail profile as the input of the proxy model, and has not yet considered the impact of other random inputs of the vehicle and track on the vehicle vibration response and wheel-rail wear under complex operating conditions. Therefore, the input dimension of the existing proxy model is low, and the conventional proxy model, similar to the Kriging and Gaussian regression process, can satisfy the proxy between the rail profile and the vehicle dynamic response. When considering the random input variables of the vehicle-track system, the input dimension of the proxy model will also increase significantly, and it is difficult to meet the calculation accuracy of the proxy model under high-dimensional variables using the above proxy model.

[0078] Due to the significant difference in measurement units, the scales (units) of sample features vary greatly, resulting in changes in values. To address this problem, the maximum and minimum normalization method is used to preprocess the sample data to create a scale-sensitive neural network proxy model. This process involves converting feature parameters of different dimensions to the same numerical range, thereby effectively reducing the differences between features. The maximum and minimum normalization method is crucial to improving the model training effect and algorithm convergence speed.

[0079] The neural network agent model has two hidden layers, and the determination of the number of nodes (m, n) is crucial to the success of model training. When the number of nodes in the hidden layer is too small, the network may lack sufficient information to solve the problem, resulting in relatively large training and test errors. On the contrary, too many nodes will lead to overfitting problems, increase training time and reduce generalization ability. In addition, the learning rate parameter (η) significantly affects the convergence speed of the model. If the learning rate is too small, the optimization process will be slow. On the other hand, if it is too large, the network may exceed the minimum and fall into a local minimum.

[0080] Further, step S400 also includes steps S450 to S470;

[0081] Step S450: Optimizing the number of hidden layer nodes and learning rate parameters of the neural network proxy model based on the predator algorithm;

[0082] Step S460: After the optimization of the number of hidden layer nodes and the learning rate parameters is completed, the initial weights and bias items of the neural network proxy model are further optimized based on the particle swarm algorithm;

[0083] Step S470: After the initial weights and bias items are optimized, the optimized neural network proxy model is obtained.

[0084] It is understandable that if Figure 4 As shown in Figure 1, in order to determine the appropriate parameters of the neural network proxy model, the predator algorithm is introduced to optimize the number of nodes (m, n) and the learning rate parameter (η), where C and Z represent the balance point between exploration and utilization and the adaptive parameter, respectively. In addition, during the training and validation process, the neural network proxy model continuously updates the weights and bias terms, making the initial selection of these parameters crucial. Based on the optimization of the number of nodes and learning rate mentioned above, the neural network proxy model also uses a particle swarm intelligent optimization algorithm. The optimization process is as follows: Figure 5 As shown in Figure 1, the algorithm takes into account the importance of the input variable features to optimize the weights and bias terms of the connections in each layer. It should be noted that due to the limited number of samples in the dataset, there is a risk of overfitting as the network depth increases. Therefore, the optimization of the neural network depth is not performed.

[0085] like Figure 6-Figure 7 The figure shows the error distribution of predicting the long-term wear performance of the rail and the dynamic response of the wheel-rail. It can be seen from the figure that the rail wear depth varies from 1.4mm to 4.8mm, and the wheel-rail lateral contact force varies from 18kN to 32kN. The prediction accuracy of the long-term wear depth of the rail is the highest, followed by the wheel-rail lateral contact force. For the performance indicators, most samples are located near the y=x line, with an error within 1%.

[0086] Furthermore, in step S100, after the proxy model is optimized, the following steps are further included:

[0087] Step S411, generating a plurality of samples from the vehicle parameter variable range through Latin hypercube, and randomly dividing the plurality of samples into a training set and a test set in a ratio of 8:2;

[0088] Step S412, the optimized neural network proxy model and multiple different proxy models respectively represent the coupled dynamics simulation model;

[0089] Step S413, using the training set to train the optimized neural network proxy model and a plurality of different proxy models, and obtaining performance comparison results on the training set based on the dynamic response results of the coupled dynamics simulation model;

[0090] Step S414, using the test set to test the optimized neural network proxy model and a plurality of different proxy models, and obtaining performance comparison results on the test set based on the dynamic response results of the coupled dynamics simulation model;

[0091] Based on the performance comparison results of the optimized neural network proxy model and a variety of different models on the training set and the test set, the accuracy of the proxy model is verified. It can be understood that in order to verify the accuracy of the optimized neural network proxy model, the radial basis function model, the Kriging interpolation model, the neural network proxy model, the support vector machine model, the random forest model and the optimized neural network proxy model are evaluated and compared based on the error evaluation index. First, 1000 samples are generated in the design space. Then, the dynamic response results under different working conditions are obtained based on numerical simulation. Finally, these samples are randomly divided into training sets and test sets in a ratio of 8:2, with 800 samples in the training set and 200 samples in the test set.

[0092] like Figure 8-Figure 9 As shown in the figure, the performance results of the six models on the training data set and the test data set are intuitively shown, where RBF represents radial basis function, Kriging represents Kriging function, BP represents back propagation neural network, SVM represents support vector machine, RF represents random forest, HPO-PSO-BP represents predator algorithm-particle swarm algorithm-back propagation neural network, MSE represents mean square error, RMSE represents root mean square error, MAE represents mean absolute error, MAPE represents mean absolute percentage error, R 2The results show that the error index of the optimized neural network proxy model is only slightly higher than that of the random forest model on the training dataset. However, in the test dataset, the optimized neural network proxy model outperforms all other models, with the lowest error index and the highest determination coefficient. In addition, the random forest model exhibits overfitting.

[0093] The optimized neural network proxy model adopts a modulation and coding strategy, which is used to convert the uncertainty of the input into the uncertainty in the result. The optimized neural network proxy model using the modulation and coding strategy can quickly calculate the dynamic response results of multiple groups of random samples and the probability distribution of rail wear, quantify the uncertainty of the vehicle safety index and the rail wear index under different optimization solutions, and obtain the random distribution of the safety index and the wear index under different optimization solutions.

[0094] Further, step S600 includes steps S610 to S630:

[0095] Step S610: setting an optimization target based on the sensitive variables and the preset design variables, wherein the optimization target includes the robustness of rail wear resistance and the robustness of lateral wheel-rail interaction;

[0096] Step S620, performing robust optimization design on the rail profile according to the optimization target;

[0097] Step S630: The robust optimization design adopts a robust optimization method based on three sigma.

[0098] It can be understood that the robust optimization design adopts the robust optimization method based on three sigma, and the robust optimization method includes:

[0099] Optimization goal:

[0100] ;

[0101] in, It is the accumulated wear of the rail profile after the vehicle passes through the small radius curve multiple times; is the lateral wheel-rail force after the vehicle passes through a small radius curve multiple times; is the wear depth; represents standard deviation;

[0102] ;

[0103] ;

[0104] ;

[0105] in, Represents the input value, is the random variable of the vehicle-track system; To optimize the design variables on the high rail side; To optimize the design variables on the LRT side;

[0106] constraint:

[0107] ;

[0108] ;

[0109] ;

[0110] ;

[0111] ;

[0112] ;

[0113] in, is the slope of the tangent line at the starting point of the optimization area; is the slope of the tangent line at the end point of the optimization region; is the tangent slope at the boundary point of the trajectory contour in the optimization area; is the tangent slope at the boundary point of the trajectory contour in the non-optimized area; is the maximum value of the derailment coefficient; is the maximum value of wheel load reduction rate; is the maximum value of wheel-rail lateral force; is the maximum value of wheel-rail vertical force; Is the connection Data points and Data points The slope of the straight line; is the design variable for the geometric discretization of rail profile; is the lateral wheel-rail force; is the vertical wheel-rail force; is the left vertical wheel-rail force; is the right vertical wheel-rail force; is the static wheel weight of one side wheel; is the static axle weight, is the wear depth.

[0114] The rail profile is optimized based on the robust optimization method. In order to reduce the discreteness of the vehicle-track dynamic response caused by the fluctuation of vehicle or track parameters, the robust optimization design considers the mean and standard deviation of the design variables. The traditional robust optimization method based on 3-sigma (3σ) is adopted. According to the optimization strategy, the multi-objective robust optimization of the rail profile is carried out for the robustness of the rail wear resistance and the robustness of the lateral wheel-rail interaction.

[0115] Fig.10 is a schematic diagram of the slope relationship of data points on the rail profile, where , , ... are continuous and discrete data points on the rail profile curve. According to the characteristics of the convex curve, the following method can be used for judgment: .in, Is the connection Data points and Data points The slope of the straight line. During the optimization process, the curves and their slopes in the optimization region will change. The continuity of the track line connecting the optimization region and the non-optimization region leads to splicing continuity, which is written as:

[0116] ;

[0117] ;

[0118] in, and are the tangent slopes at the start and end of the optimization region, and are the tangent slopes at the boundary points of the trajectory contour in the optimized area and the non-optimized area, respectively.

[0119] When optimizing the rail section, the design parameters are continuously adjusted until the designed rail section meets the optimization goal. Therefore, choosing the appropriate profile description method and constructing certain design parameters are crucial for the optimal rail profile design. The rail section consists of curves with different curvatures, and the curves must be smooth and continuous. Since the rail section after wear is an irregular free curve, NURBS curves are used here as a unified mathematical form to describe standard analytical curves and free curves. Since NURBS curves have local adjustment, concave and convex shapes, and smooth and continuous geometric characteristics, they can meet the requirements of parametric modeling of worn rails. Therefore, cubic NURBS curves are used for curve fitting of worn rail profiles and provide a basis for creating new track profiles based on design variables.

[0120] In order to consider the uncertainty of vehicle and track parameters under actual operating conditions, the multi-objective robust optimization is used to optimize the small radius curve rail profile. The Pareto frontier of multi-objective deterministic and robust optimization is obtained, as shown in Fig.11 As shown in Figure 2, the Pareto front of the robust optimization is located to the right of the corresponding Pareto front obtained by the deterministic optimization. This shows that the robust optimization moves the optimal design further away from the constraints, thereby reducing the possibility of constraint violations caused by changes in design parameters. Designers can obtain the optimal design value directly from the Pareto front according to engineering requirements. For example, if the wear depth should be limited to less than 3 mm, the optimal value of the multi-objective deterministic and robust optimization is Fig.11 The solid squares and triangles are marked in the figure.

[0121] Further, step S500 includes steps S510 to S530:

[0122] Step S510, performing Monte Carlo simulation on the random samples to generate prediction samples;

[0123] Step S520: using the prediction sample as an input value of the dynamic response prediction model to obtain a prediction result;

[0124] Step S530: generating a vehicle dynamic response index under a random operating condition based on the prediction result, wherein the vehicle dynamic response index includes a probability density distribution result of wheel-rail force, derailment coefficient, wheel load reduction rate and rail wear depth.

[0125] Furthermore, step S600 also includes steps S640 to S670:

[0126] Step S640, selecting the mean value of the vehicle-track system parameter variable as the input of the dynamic response simulation model;

[0127] Step S650, the tested original rail profile and the optimized rail profile are simulated by the dynamic response simulation model respectively, and the simulation results include the lateral wheel-rail force, derailment coefficient and wear work of the wheelset;

[0128] Step S660, comparing the lateral wheel-rail force, derailment coefficient and wear work on the high rail side of the original rail profile and the optimized rail profile, as well as the lateral wheel-rail force, derailment coefficient and wear work on the low rail side;

[0129] Step S670: Determine by comparison whether the optimized rail profile improves safety performance and lateral wheel-rail dynamic performance.

[0130] The effectiveness of the optimized rail profile is evaluated by comparing the original rail profile and the optimized rail profile. Figure 14-15shown.

[0131] For each rail profile optimization design, the optimized neural network proxy model was simulated and run 10,000 times to estimate the average results of vehicle dynamic response and rail wear index. The distribution of the 10,000 simulation results is shown in Figure 2. Fig.12 and Fig.13 As shown in the figure. Each scenario has two marginal probability density functions of rail cumulative wear depth and transverse wheel-rail force. The probability density function can tell the decision makers of railway maintenance and repair how likely it is that a specific value or a specific range of model output will be observed, and a comprehensive decision can be made based on the probability density distribution.

[0132] Compared with the responses before and after optimization, the mean and variance of the cumulative rail wear depth, lateral wheel-rail force and derailment coefficient are greatly reduced. However, the probability density distribution of wheel weight reduction rate does not change significantly before and after optimization. This shows that the optimized profile has a significant effect on the lateral wheel-rail interaction and rail wear in the curved section. Based on the comparison of the optimization results in the two cases, whether the variance of the design parameters is used as a controllable parameter will depend on the specific engineering design situation.

[0133] In order to compare the dynamic characteristics of the original rail profile and the optimized rail profile, the mean value of the vehicle-track system parameter variables was selected as the input of the dynamic response simulation model, and the curve passing simulation was performed for the original rail profile and the optimized rail profile. The vehicle speed was 60km / h, the curve radius was 400 meters, and the curve superelevation was 100mm. The simulation results include the lateral wheel-rail force, derailment coefficient and wear work of the first wheel pair, such as Figure 15-17 As shown. It can be seen that the optimization of the rail section reduces the derailment coefficient on the high rail side by 21.83% and the derailment coefficient on the low rail side by 28.31%, thereby significantly improving the safety of vehicles passing through curves. The wheel-rail lateral force and wear index on the high rail side are reduced by 31.22% and 43.75%, respectively. Therefore, the optimized track profile also significantly improves the lateral wheel-rail dynamic performance. Compared with the original rail profile, the optimized rail profile can effectively improve the bending performance of vehicles on small radius curves.

[0134] It should be explained that a value of zero refers to the exact center of the wheel, and a negative value refers to a contact point in the flange area. For each wheelset, when using the optimized rail profile, the wheel-rail contact point on the high rail side moves from the tread to the top of the flange. This means that the possibility of contact in the flange area is reduced, so the wear of both the rail side and the wheel flange is reduced.

[0135] In order to more intuitively analyze the optimization effect of severely worn rails and compare whether the optimized rail profile can extend the service life of the rails, the wear evolution of the rails before and after optimization was carried out. Figure 18-19As shown in the figure, as the number of train passes increases, the cumulative wear increases. Before optimization, the rail wear range was [-31, -10], and the maximum cumulative wear was 2.82 mm when the vehicle passed 100,000 times. After optimization, the maximum cumulative wear was 1.48 mm when the vehicle passed 100,000 times, which was 8.44% lower than before optimization. The maximum cumulative wear was 2.40 mm when the vehicle passed 200,000 times, which was 47.5% lower than before optimization. This shows that the more times the vehicle passes, the less cumulative wear is than before optimization. The multi-objective robust optimization strategy has achieved the effect of extending the service life of the rails.

[0136] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

[0137] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A robust optimization design method for asymmetric rail profile on a small-radius railway curve, characterized in that: include: Obtaining a wear variable range of rail profile geometry, a vehicle parameter variable range, and a track parameter variable range, and generating multiple groups of random samples through Latin hypercube according to the wear variable range, the vehicle parameter variable range, and the track parameter variable range; Constructing a coupled dynamics simulation model of a vehicle-track system according to the random samples, and outputting key indicators by simulating the dynamic response of the vehicle-track system, wherein the key indicators include the wheel-rail force, derailment coefficient, wheel load reduction rate and rail wear of each of the random samples; Calculating the rail cumulative wear depth data under different random variable combinations according to the key indicators and the preset wear model; A proxy model is constructed according to the random sample, the key index and the rail cumulative wear depth data, and the proxy model is optimized, and the coupled dynamics simulation model is substituted by the optimized proxy model to obtain a dynamic response prediction model; The random samples are used as input values ​​of the dynamic response prediction model, and the probability density distribution results of the rail wear performance and the wheel-rail dynamic response are obtained by predicting the dynamic response and wear depth under random working conditions, and a sensitivity analysis is performed on the probability density distribution results to obtain sensitive variables that affect the optimization target; Constructing a multi-objective function according to the sensitive variables and the preset design variables to generate a Pareto front solution, and obtaining a rail profile optimization design scheme based on the Pareto front solution fitting; Wherein, constructing a multi-objective function according to the sensitive variables and the preset design variables to generate a Pareto front solution, and obtaining a rail profile optimization design scheme based on the Pareto front solution fitting, including: Setting optimization targets based on the sensitive variables and preset design variables, wherein the optimization targets include the robustness of rail wear resistance and the robustness of lateral wheel-rail interaction; According to the optimization target, a robust optimization design is performed on the profile of the rail to obtain an optimization design scheme for the rail profile; The robust optimization design adopts a robust optimization method based on three sigma; Wherein, the optimization goal is: min.u[f1(x)]+3σ[f1(x)] u[f2(x)]+3σ[f2(x)] Where f1(x) is the cumulative wear of the rail profile after the vehicle passes through a small radius curve multiple times; f2(x) is the lateral wheel-rail force after the vehicle passes through a small radius curve multiple times; u is the wear depth; σ represents the standard deviation; x=[z li ,z ri ,r] With li =[of l1 ,With l2 ,…,With ln ] With ri =[of r1 ,With r2 ,…,With rn ] Where x represents the input value, r is the random variable of the vehicle-track system; z li To optimize the design variables on the high rail side; ri To optimize the design variables on the LRT side; constraint: k ys =k1 k ye =k n k i >k i+1 Among them, k ys k is the slope of the tangent line at the starting point of the optimization area; ye is the tangent slope at the end point of the optimization region; k1 is the tangent slope at the boundary point of the trajectory contour of the optimization region; k n is the tangent slope at the boundary point of the track profile in the non-optimized area; g1 is the maximum derailment coefficient; g2 is the maximum wheel-load reduction rate; g3 is the maximum wheel-rail lateral force; g4 is the maximum wheel-rail vertical force; k i is to connect the i-th data point m i and the i+1th data point m i+1 The slope of the straight line; z is the design variable of the rail profile geometry discretization; Y is the lateral wheel-rail force; Q is the vertical wheel-rail force; Q l is the left vertical wheel-rail force; Q r is the right vertical wheel-rail force; Q0 is the static wheel weight of one side wheel; P0 is the static axle weight, and u is the wear depth.

2. The method for optimizing the robustness of asymmetric rail profile for railway small radius curves according to claim 1 is characterized in that: Obtain the range of wear variables for rail profile geometry, including: By analyzing the contact geometry between the rail profile and the wheelset, the optimized area parameters of the rail profile are obtained; Establishing a rail profile discrete coordinate system based on the optimization area parameters; Discretely setting the optimization area parameters as a plurality of movable points in the rail profile discrete coordinate system, wherein the lateral coordinates of the movable points are fixed and the vertical coordinates of the movable points are variable; According to the preset variable range of the vertical coordinate of the movable point, the variable range of the vertical coordinate of the movable point is used as the wear variable range of the rail profile geometry.

3. The method for optimizing the robustness of asymmetric rail profile for railway small radius curves according to claim 1 is characterized in that: A coupled dynamics simulation model of a vehicle-track system is constructed according to the random samples, including: Obtain vehicle parameters and track design parameters, and build a vehicle model based on the vehicle parameters, and build a track model based on the track design parameters; The body, frame and wheelset of the vehicle model are all set as steel bodies, and the primary suspension and secondary suspension of the vehicle model are simulated according to the spring damping unit in the multi-body dynamics analysis software package; The vehicle model and the track model are coupled to obtain the coupled dynamics simulation model, the coupled dynamics simulation model uses the Hertz nonlinear contact algorithm for dynamics simulation, and the wheel-rail tangential contact of the coupled dynamics simulation model is solved by the Fastsim fast simulation algorithm.

4. The method for optimizing the robustness of asymmetric rail profile for railway small radius curves according to claim 1 is characterized in that: According to the key indicators and the preset wear model, the rail cumulative wear depth data under different random variable combinations are calculated, including: Constructing an Archad wear model based on the key indicators; The material wear behavior of the Archad wear model is set to occur only in the contact spot sliding area of ​​the rail profile, and no wear occurs in the adhesion area of ​​the rail profile; Divide the contact spot sliding area of ​​the rail profile into N grids, and solve the accumulated wear amounts in the N grids respectively; Based on the accumulated wear amounts in the N grids, the accumulated rail wear depth data of the rail profile under random operating conditions is obtained.

5. The method for optimizing the robustness of asymmetric rail profile for railway small radius curves according to claim 1 is characterized in that: Building a proxy model based on the random sample, the key indicator and the rail cumulative wear depth data includes: A neural network proxy model is constructed based on the random sample, the key index and the rail cumulative wear depth data, wherein the neural network proxy model consists of an input layer, two hidden layers and an output layer, and the neural network proxy model uses a maximum-minimum normalization method to preprocess the sample data; Obtaining 80% of the random samples of the key indicators to train the neural network proxy model, and obtaining the objective function and constraint function of the neural network proxy model; Obtaining 20% ​​of random samples of the key indicators to test the prediction accuracy of the neural network agent model; Based on a preset error range, it is determined whether the constructed proxy model is valid. If the prediction accuracy is within the error range, the constructed proxy model is valid; if the prediction accuracy is outside the error range, the constructed proxy model is invalid.

6. The method for optimizing the robustness of asymmetric rail profile for railway small radius curves according to claim 5 is characterized in that: Performing proxy model optimization on the proxy model includes: Based on the predator algorithm, the number of hidden layer nodes and the learning rate parameters of the neural network proxy model are optimized; After completing the optimization of the number of hidden layer nodes and the learning rate parameters, further optimizing the initial weights and bias items of the neural network proxy model based on the particle swarm algorithm; After the initial weights and bias items are optimized, the optimized neural network proxy model is obtained.

7. The method for optimizing the robustness of asymmetric rail profile for railway small radius curves according to claim 6 is characterized in that: After the proxy model is optimized, the accuracy of the proxy model is verified: The vehicle parameter variable range is used to generate a plurality of samples through Latin hypercube, and the plurality of samples are randomly divided into a training set and a test set in a ratio of 8:2; The optimized neural network proxy model and a plurality of different proxy models respectively represent the coupled dynamics simulation model; Using the training set to train the optimized neural network proxy model and a plurality of different proxy models, and obtaining performance comparison results on the training set based on the dynamic response results of the coupled dynamics simulation model; Using the test set to test the optimized neural network proxy model and a plurality of different proxy models, and obtaining performance comparison results on the test set based on the dynamic response results of the coupled dynamics simulation model; Based on the performance comparison results of the optimized neural network proxy model and a variety of different models on the training set and the test set, the accuracy of the proxy model is verified.

8. The method for optimizing the robustness of asymmetric rail profile on a railway small radius curve according to claim 1 is characterized in that: The random samples are used as input values ​​of the dynamic response prediction model, and the probability density distribution results of the rail wear performance and the wheel-rail dynamic response are obtained by predicting the dynamic response and wear depth under random working conditions, including: Performing Monte Carlo simulation on the random samples to generate prediction samples; Using the prediction sample as an input value of the dynamic response prediction model to obtain a prediction result; Based on the prediction results, a vehicle dynamic response index under a random operating condition is generated, and the vehicle dynamic response index includes probability density distribution results of wheel-rail force, derailment coefficient, wheel load reduction rate and rail wear depth.

9. The method for optimizing the robustness of asymmetric rail profile on a railway small radius curve according to claim 1, characterized in that: After obtaining the optimized design of rail profile, the dynamic characteristics of the original rail profile and the optimized rail profile are also compared: Selecting the mean value of the vehicle-track system parameter variables as the input of the dynamic response simulation model; The original rail profile and the optimized rail profile tested are simulated by the dynamic response simulation model respectively, and the simulation results include the lateral wheel-rail force, derailment coefficient and wear work of the wheelset; Compare the lateral wheel-rail force, derailment coefficient and wear work on the high rail side of the original rail profile and the optimized rail profile, as well as the lateral wheel-rail force, derailment coefficient and wear work on the low rail side; Compare and judge whether the optimized rail profile improves the safety performance and lateral wheel-rail dynamic performance.

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